Re: IDEALIZATIONS, was textbook touchstones

[Joel Rauber <Joel_Rauber@SDSTATE.EDU>]

"Equal charge law"

> But Q1 and Q2 on two capacitors in series are never equal, unless
> leakage resistances happen to coincide. Everybody knows this but
> for some strange reason the authors of textbook keep repeating that
> Q1=Q2. It is not a relation which becomes more and more correct
> as a function of DOP or of some other factor.

The issues are more involved than just questions of leakage current.

Even if no leakage current is present, i.e. the dielectric material in
between the plates are perfect insulators; Q1 may still not equal Q2, or at
least I've seen no proof that I like that does not involve significant
geometric idealizations.

The proofs, not often described in texts, other than to assert the result;
rely on all field lines originating on the positively charged plate
terminating on the negatively charged plate of the *same* capacitor.  I
gather that this can be rigoruously true for the ideal infinite area
parallel plate capacitors and perhaps some other such highly idealized and
symmetric situations.  How true is this for real capacitors in circuits?
Probably true enough for government work in the absence of leakage currents?
(comment based on speculation, not on any data I've taken)

Regarding the 9th incarnation of Sears & Zemansky that Sandin referred to
(which BTW we are currently teaching out of, and my opinion is that it is a
rather good intro book):

Their "proof" of the "equal charge law", while better than many books, IMHO,
because it mentions the field line staement above, thereby offering a reason
why the charge on the inner charged plates of the two capacitors should be
the same as the outer plates (the ones directily connected to the voltage
source that is causing all this charge seperation); never-the-less does not
mention the idealizations involved in making that statement.

IMHO, all these considerations put the equal charge law in the class of
"very useful rules of thumb".  And is a different type of idealization from,
say, massless pulleys. Since it requires ideal geometries in addition to
ideal materials.

This is all rather off the cuff, so I hope to illicit more discussion and
folks pointing out the errors of my ways.

Joel Rauber